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1 year ago

In Exploration 5.4.2 Question 2, what conclusion can you make about the value of the derivative at

Mathematics

1 answer:

givi [52]1 year ago

4 0

The value of the derivative at the maximum or minimum for a continuous function must be zero.

<h3>What happens with the derivative at the maximum of minimum?</h3>

So, remember that the derivative at a given value gives the slope of a tangent line to the curve at that point.

Now, also remember that maximums or minimums are points where the behavior of the curve changes (it stops going up and starts going down or things like that).

If you draw the tangent line to these points, you will see that you end with horizontal lines. And the slope of a horizontal line is zero.

So we conclude that the value of the derivative at the maximum or minimum for a continuous function must be zero.

If you want to learn more about maximums and minimums, you can read:

brainly.com/question/24701109

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Which equation is the inverse of y = 9x2 - 4?

m_a_m_a [10]

Answer:

The inverse will be:

$y' = \frac{\sqrt{x+4}}{3}$

Step-by-step explanation:

In order to find the inverse of the equation, we do a variable change, since we are finding the inverse, :

$f(x) = 9x^{2} - 4$

$y = 9x^{2} - 4$

$x = 9y' ^{2} - 4$

Now solve for y'.

First add 4 in both sides of the equation and change to the left y'.

$x + 4= 9y'^{2} - 4+4$

$9y'^{2}$ = x + 4

Second divide by 9

$9y'^{2}$ /9 = (x + 4)/9

$y'^{2}$ = (x + 4)/9

Now you will have to clear y, with the square root.

$[tex]y'^{\frac{2}{2}} = \sqrt{x + 4} / \sqrt{9}$ [/tex] =

Simplifying terms

$y' = \frac{\sqrt{x+4}}{3}$

$f^{-1}(x) = \frac{\sqrt{x+4}}{3}$

You can check the answer by doing the evaluation of the following equation:

(f o $f^{-1}$ ) (x)

substitute the equation for y' or inverse function $f^{-1}$

f( $\frac{\sqrt{x+4} }{3}$ )

Now substitue the value into f(x)

You will have

$= 9(\frac{\sqrt{x+4} }{3}} )^{2} - 4\\\\Solving\\\\9(\frac{{x+4} }{9}} ) - 4$

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2 years ago

Please select the best answer from the choices provided ASAP

LuckyWell [14K]

Answer:

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Write a word phrase that can be represented by b - 37

Charra [1.4K]

A number decreased by thirty seven or thirty seven less than a number

6 0

2 years ago

The function f is given by f(x) = 3x² - 5<br> -<br> a) Work out f '(43)

Lana71 [14]

Answer:

5236

Step-by-step explanation:

let x=43

f(43)=3(43)^2-5

f(43)=3(1749)-5

f(43)=5241-5

f(43)=5236

4 0

2 years ago

Empirical rule (statistics)Help please!!!

emmasim [6.3K]

The empirical rule you're referring to is the 68-95-99.7 rule, which asserts that for a normal (bell-shaped) distribution, approximately 68% of the distribution lies within 1 standard deviation of the mean; 95% lies within 2 standard deviations of the mean; and 99.7% lies within 3 standard deviations of the mean.

Let $X$ be the random variable denoting vehicle speeds along this highway. We want to find $P(61$ . To use the rule, we need to rephrase this probability in terms of the mean and standard deviation.

Notice that $61=70-9=70-3\cdot3$ , and $79=70+9=70+3\cdot3$ . In other words, 61 and 79 both lie exactly 3 standard deviations away from the mean, so $P(61$ .

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2 years ago